在排好序的数组 [1, 3, 6, 9, 17, 31, 39, 52, 61, 79, 81, 90, 96] 中查找数值82，二分查找代码如下：

int binary_search(vector<int>& nums, int target) {
    int left = 0;
    int right = nums.size() - 1;
    while (left <= right) {
        int mid = (left + right) / 2;
        if (nums[mid] == target) {
            return mid;
        } else if (nums[mid] < target) {
            left = mid + 1;
        } else {
            right = mid - 1;
        }
    }
    return -1; // 如果找不到目标元素，返回-1
}